Can the linear combination of atomic orbital coefficients (the weight function) be used to improve the wavefunction?

1993 ◽  
Vol 281 (1) ◽  
pp. 75-87 ◽  
Author(s):  
R. Custodio ◽  
J.D. Goddard
Keyword(s):  
Weight Function ◽  
Linear Combination ◽  
Atomic Orbital

Déplacement chimique du proton en résonance magnétique nucléaire. I. Calcul du terme diamagnétique en vue de son utilisation à l'étude de la structure des molécules. Application aux éthers vinyliques

1970 ◽  
Vol 48 (20) ◽  
pp. 3154-3163 ◽  
Author(s):  
François Tonnard ◽  
Simone Odiot ◽  
Maryvonne L. Martin
Keyword(s):  
Carbon Atom ◽  
Linear Combination ◽  
Atomic Orbital ◽  
Ethoxy Group ◽  
Vinyl Ethers ◽  
Résonance Magnétique

A relation between the diamagnetic term for a proton bonded to a carbon atom and the linear combination of atomic orbital charges on C and H is established. Proton diamagnetic terms of some vinyl ethers are calculated, and the conformation of ethoxy group in these molecules studied.

scholarly journals Optimized Probes of the CP Nature of the Top Quark Yukawa Coupling at Hadron Colliders

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1129
Author(s):  
Darius A. Faroughy ◽  
Blaž Bortolato ◽  
Jernej F. Kamenik ◽  
Nejc Košnik ◽  
Aleks Smolkovič
Keyword(s):  
Machine Learning ◽  
Higgs Boson ◽  
Phase Space ◽  
Weight Function ◽  
Pair Production ◽  
Linear Combination ◽  
Top Quark ◽  
Hadron Colliders ◽  
Optimal Linear ◽  
Hadronic Process

We summarize our recent proposals for probing the CP-odd iκ˜t¯γ5th interaction at the LHC and its projected upgrades directly using associated on-shell Higgs boson and top quark or top quark pair production. We first recount how to construct a CP-odd observable based on top quark polarization in Wb→th scattering with optimal linear sensitivity to κ˜. For the corresponding hadronic process pp→thj we then present a method of extracting the phase-space dependent weight function that allows to retain close to optimal sensitivity to κ˜. For the case of top quark pair production in association with the Higgs boson, pp→tt¯h, with semileptonically decaying tops, we instead show how one can construct manifestly CP-odd observables that rely solely on measuring the momenta of the Higgs boson and the leptons and b-jets from the decaying tops without having to distinguish the charge of the b-jets. Finally, we introduce machine learning (ML) and non-ML techniques to study the phase-space optimization of such CP-odd observables. We emphasize a simple optimized linear combination α·ω that gives similar sensitivity as the studied fully fledged ML models. Using α·ω we review sensitivity projections to κ˜ at HL-LHC, HE-LHC, and FCC-hh.

Orthogonality of Certain Functions with Respect to Complex Valued Weights

1981 ◽  
Vol 33 (5) ◽  
pp. 1261-1270 ◽  
Author(s):  
George Gasper
Keyword(s):  
Dirichlet Problem ◽  
Weight Function ◽  
Heisenberg Group ◽  
Linear Combination ◽  
Generating Function ◽  
Legendre Polynomial ◽  
Spherical Harmonic ◽  
Orthogonality Relation ◽  
Image Position ◽  
Complex Valued

In his work on the Dirichlet problem for the Heisenberg group Greiner [5] showed that each Lα-spherical harmonic is a unique linear combination of functions of the formwith k = 0, 1,2, … and n = 0, ±l, ±2 , …, where Hk(α, n)(θiθ) is defined by the generating functionSince Hk(0,0)(eiθ) = Pk(cos θ), where Pk(x) is the Legendre polynomial of degree k, and these functions satisfy the orthogonality relationGreiner raised the question of whether the functions Hk(0,0)(eiθ) are orthogonal or biorthogonal with respect to some complex valued weight function.

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